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(Steps Shown) Consider the quadratic form Q(x, y, z)=3 x^2+8 x z+2 y^2+3 z^2. Is this quadratic form positive definite? Find the symmetric matrix A for

Question: Consider the quadratic form \(Q(x, y, z)=3 x^{2}+8 x z+2 y^{2}+3 z^{2}\). Is this quadratic form positive definite? Find the symmetric matrix \(A\) for which

\[Q(x, y, z)=\left(\begin{array}{lll} x & y & z \end{array}\right) A\left(\begin{array}{l} x \\ y \\ z \end{array}\right)\]

and then find the eigenvalues of \(A\). To say that \(Q\) is positive definite means that all of the eigenvalues of \(A\) are positive.

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